Three forces P, Q and R act at the same point and are in equilibrium. The forces P and Q have magnitudes 30 N and 20 N respectively, and there is an angle of 20° between their directions. Calculate the magnitude of the force R?

↳Redirected from "Suppose that I don't have a formula for #g(x)# but I know that #g(1) = 3# and #g'(x) = sqrt(x^2+15)# for all x. How do I use a linear approximation to estimate #g(0.9)# and #g(1.1)#?"
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A08
May 15, 2018

Three forces #vecP, vecQ and vecR# act at the same point and are in equilibrium.
Given forces #vecP and vecQ#.
#=># Resultant of #vecP and vecQ# is equal and opposite to #vecR#

By Parallelogram Law of vectors, magnitude of resultant #vecR_r# of two vectors #vecP and vecQ# is given by the expression

#|vecR_r|=sqrt(|vecP|^2+|vecQ|^2+2|vecP||vecQ|cos alpha)#
where, #alpha# is the angle between the two.

Inserting given values we get

#|vecR_r|=sqrt(30^2+20^2+2xx30xx20\ cos 20^@)#
#=>|vecR_r|=sqrt(900+400+1200xx0.93969)#
#=>|vecR_r|=49.3\ N#
#:.|vecR|=49.3\ N#

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